Theorems · Theorem · commutative algebra
DirectSum.toBaseChange_bijective
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {S : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] (ℳ : ι → Submodule R M) [inst_3 : DecidableEq ι] [DirectSum.Decomposition ℳ]
[inst_5 : CommSemiring S] [inst_6 : Algebra R S] (i : ι), Function.Bijective ⇑(Submodule.toBaseChange S (ℳ i))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement · cited by 2,545
- Function.Bijectivestatement · cited by 863
- DirectSum.Decompositionstatement and proof · cited by 57
- Submodule.baseChangestatement · cited by 36
Cited by1
Results whose statement or proof uses this declaration.
- DirectSum.IsInternal.toBaseChange_bijectiveproof · cited by 1